Universal robustness of scale-free networks against cascading edge failures

Abstract

Considering the effect of the local topology structure of an edge on cascading failures, we investigate the cascading reaction behaviors on scale-free networks with respect to small edge-based initial attacks. Adopt the initial load of an edge ij in a network to be Lij = (kikj)α[(∑ka)(∑kb)]β with ki and kj being the degrees of the nodes connected by the edge ij, where α and β are tunable parameters, governing the strength of the edge initial load, and Γi and Γj are the sets of neighboring nodes of i and j, respectively. Our aim is to explore the relationship between some parameters and universal robustness characteristics against cascading failures on scale-free networks. We find by the theoretical analysis that the Baraba'si-Albert (BA) scale-free networks can reach the strongest robustness level against cascading failures when α + β = 1, where the robustness is quantified by a transition from normal state to collapse. And the network robustness has a positive correlation with the average degree. We furthermore confirm by the numerical simulations these results.